Imaginary-Time Formulation of Steady-State Nonequilibrium: Application to Strongly Correlated Transport

We extend the imaginary-time formulation of the equilibrium quantum many-body theory to steady-state nonequilibrium with an application to strongly correlated transport. By introducing the Matsubara voltage, we maintain the finite chemical potential shifts in the Fermi-Dirac function, in agreement with the Keldysh formulation. The formulation is applied to strongly correlated transport in the Kondo regime using the quantum Monte Carlo method.

Figure 1

(a) Second order perturbation self-energy at ($i{\omega }_n$, $i{\phi }_m$) with Matsubara voltage ${\phi }_m=4m\pi /\beta$. (b) Analytic continuation $i{\phi }_m\to \Phi$ performed based on the fit, Eq. (16). The result agrees very well with the exact continuation from the analytic expression. (c) Self-energy calculated from the quantum Monte Carlo method. (d) Spectral function $A(\omega )$ of the QD Green function. The Kondo peak quickly disappears as the bias $\Phi$ is increased and develops into two broad peaks at $\omega \sim \pm \Phi$.

Figure 2

The dc conductance of the Kondo quantum dot system. The width of the anomalous peak is significantly narrower than what the zero-bias spectral function predicts [$A_{\mathrm{eq}}(\omega ,\Phi =0)$ with $\omega$ scaled according to $\Phi /2$, short-dashed line], due to the destruction of Kondo resonance at finite bias $\Phi$. In the strongly correlated regime ($U=10$), the Kondo peak becomes more pronounced with strong temperature dependence. At $\Phi \sim U/2$ and $U$, the broad inelastic transport peak emerges. The noninteracting limit ($U=0$) is shown as a thin line.